Misspecified Beliefs about Time Lags

TL;DR

This paper investigates how a Bayesian agent with incorrect beliefs about action-feedback delays learns over time, revealing that such misspecifications can cause long-term inefficiencies especially in cyclic behaviors, with implications for policy-making.

Contribution

It introduces a novel analysis of long-term learning dynamics under misspecified time lag beliefs, using concentration inequalities to bound action switching frequencies.

Findings

Misspecified beliefs cause attribution errors without long-term effects when actions converge.

Cyclic actions under misspecification can lead to significant long-term inefficiencies.

The methods apply to policy games involving agents with correct and incorrect beliefs about delays.

Abstract

We examine the long-term behavior of a Bayesian agent who has a misspecified belief about the time lag between actions and feedback, and learns about the payoff consequences of his actions over time. Misspecified beliefs about time lags result in attribution errors, which have no long-term effect when the agent's action converges, but can lead to arbitrarily large long-term inefficiencies when his action cycles. Our proof uses concentration inequalities to bound the frequency of action switches, which are useful to study learning problems with history dependence. We apply our methods to study a policy choice game between a policy-maker who has a correctly specified belief about the time lag and the public who has a misspecified belief.